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Block-centered local refinement methods for the time-fractional equations

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  • Guo, Qing
  • Rui, Hongxing

Abstract

In this paper, we present and analyze two block-centered local refinement (BLR) methods for solving the time-fractional equations. The main difference between the two methods is that different approximation methods are used for the value of the pressure at the slave nodes. One adopts a piecewise constant interpolation approximation (PCIA) method, which is called simple block-centered local refinement (S-BLR) method. The other utilizes a piecewise linear interpolation approximation (PLIA) method, which called more accurate block-centered local refinement (MA-BLR) method. The stability analysis is proved carefully. It is estimated that the discrete L2 errors for the velocity and pressure are O(▵t2−α+h3/2) and O(▵t2−α+h3/2) in use of S-BLR and MA-BLR methods, respectively. Where Δt is the time step and h is the maximal mesh size. These error estimate results are all established on locally refinement composite grids. Finally, a numerical experiment is presented to show that the convergence rates are in agreement with the theoretical analysis.

Suggested Citation

  • Guo, Qing & Rui, Hongxing, 2021. "Block-centered local refinement methods for the time-fractional equations," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    • Handle: RePEc:eee:chsofr:v:152:y:2021:i:c:s0960077921006688
    DOI: 10.1016/j.chaos.2021.111314
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